Answers to mathematical digest 125
page 1              King Menkaura
                          King Khafre

page 3              The duration of my life so far is a dot on the timeline                                                   compared to the timeline's length of 5000 years.

Great Pyramid  3.142   Khafre Pyramid  2.990   Menkaura Pyramid  3.198

4 years, 7 months, 6 days

page 4              The Golden Ratio for the Great Pyramid = 1.61888845, for the Khafre Pyramid = 1.670, for the Menkaura Pyramid = 1.60149.

If Herodotus was correct the Golden Ratio in the Great Pyramid would be 1.621 which is less accurate than what it is.

page 6              Thales was the older. He would have been between 80 and 90 years of age when they met, probably between 560BC and 550BC.
Thales was 75 years old when the eclipse occurred in 585BC.

page 7               Thales measures the Great Pyramid    a = 416.386 m

page 8                Area = 6500 cubits
                            Bread = 238 loaves   
                            Flour  = 104 hekats
                            Beer  = 294 jugs

page 9               Height of Bent Pyramid  124.92 m
5/8 = 1/2 + 1/8
4/7 = 1/2 + 1/4
22/7 = 3 + 1/7
49/60 = 1/2 + 1/6 + 1/10 + 1/20

This is 1/16 = 1/32 + 1/48 + 1/80
This is 1/12 = 1/24 + 1/36 + 1/60
This is 1/14 = 1/28 + 1/42 + 1/70

page 10                 cannon balls    1    5    14    30    55    91    140
No with 13 rows there are 819 balls and with 14 rows there are 1015 balls
If the base measure 10 by 10 there are 385 balls in the pyramid
If the number of rows is 10 there are also 385 balls in the pyramid.

page 11        yes, it can be done! A 24 x 24 base gives a total of 4900 balls.

page 12      There are 5313 cannon balls in the pile. The base is 22 x 28.